Bounds on edge shear layer persistence while approaching the density limit

Abstract

This paper details the theory of edge shear layer collapse as the density approaches the Greenwald density limit. It significantly extends earlier work, which was restricted in applicability. The zonal shear flow screening length is calculated for banana, plateau and Pfirsch–Schluter regimes. Poloidal field scaling persists in the plateau regime. Neoclassical screening and drift wave–zonal flow dynamics are combined in a theory, which is then reduced to a predator–prey model. Zonal noise, due to incoherent mode coupling, is retained. The threshold condition for edge shear layer collapse is computed, and linked to a critical value of the dimensionless parameter ρ s / ρ s c L n . Here ρ s is the ion sound radius, ρ s c is the zonal flow screening length and L n is the equilibrium density scale length. The limiting initial edge density for shear layer collapse is derived and shown to scale favorably with the plasma current. The results are discussed in light of the density limit and Ohmic phenomenology.

How the birth and death of shear layers determine confinement evolution: from the L → H transition to the density limit

“…The key point is that higher current strengthens zonal flow shear, for fixed drive. Since the edge is of primary interest in the context of DLs, we comment here that Singh & Diamond [33] also have shown that favourable Ip scaling of the asymptotic temporal response of the zonal potential persists in the plateau regime. In particular, the current scaling is the same, though the response is numerically smaller.…”

“…These lead one to a new predator-prey model for turbulence-zonal flow evolution. Such a model was developed by Singh and Diamond in 2021 (hereafter SD1) by extending previous versions of the predator-prey model [33]. This model has features summarized in figure 14.…”

“…To extract a quantitative DL scaling, one must combine: fluctuation and zonal flow evolution,neoclassical zonal flow screening,zonal flow damping (collisional),incoherent mode coupling and modulational instability. These lead one to a new predator–prey model for turbulence-zonal flow evolution. Such a model was developed by Singh and Diamond in 2021 (hereafter SD1) by extending previous versions of the predator–prey model [33]. This model has features summarized in figure 14.…”

“…Inclusion of neoclassical zonal flow screening in the vein of the SD1 analysis recovers Greenwald scaling within the shear layer collapse paradigm.

Figure 14Extended predator–prey model, yielding current scaling of the limiting density [33]. (Online version in colour.

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“…Theoretical work focuses on linking microphysics to macroscopic scalings. Greenwald scaling is shown to follow from neoclassical dielectric screening effects on the zonal flow response [33]. A predator–prey model is developed to predict zonal flow collapse.…”